While this system does work well for very meritocratic groups, it is a mostly anecdotal/self-constructed replacement for defined/quantified hierarchy. The "influence over authority" framework is the adhoc social group hierarchy that is replacing a defined hierarchy, and is very susceptible to silos, clicks, and favoritism; regardless of the accuracy of the merit calculations by the members, of the members.
I am not knocking the system, as I agree that a meritocratic structure can work in small social systems, but there are some risk. The primary ones would be new member exclusion which can be hidden behind the meritocratic mantle of "it's the best choice", and fiefdom building that can result from the finite number of members that can function in a social group or that can reliably be recalled/indexed by members with in a group.
It may be possible to have numerous self contained and self structured groups operating within a larger organization, assuming the time tables allow for them to establish, and that new member barriers are not so obvious that they decrease retention. Facebook may be knowingly or unknowingly leveraging their Employer Brand to mitigate the risk of attrition within hierarchy-lite system.